Mathematics
Visual models of identities
सर्वसमिकाओं के दृश्य मॉडल
In Class 9 Mathematics, under the chapter Exploring Algebraic Identities, students use geometric diagrams and area-based representations to understand algebraic identities visually. They relate squares and rectangles formed from algebraic expressions to expansions such as binomial products, helping them see why both sides of an identity are equal rather than merely memorising formulas.
Practice questions
A visual model rearranges (x^2-y^2) into a rectangle of height (x-y). What will be its length?ExpertLevel 66When the square of side (x-y) is subtracted from the square of side (x+2y), what area does the visual model give?ExpertLevel 66In a square of side (a+b), the strip involving (b) is shaded. If the total shaded part is (2ab+b^2), what is the unshaded part?ExpertLevel 66Which tile combination gives a visual proof that (x^2-64=(x-8)(x+8))?ExpertLevel 66A rectangle model has total area (12x^2+17x-5). Which grid sides can be correct?ExpertLevel 66A large square has side (p+q), and inside it is a square of side (p-q). What is the area of the border strip between them?ExpertLevel 66If in the rectangle model of ((x+a)(x+b)), (ab=42) and the sum of middle strips is (13x), what can (a) and (b) be?ExpertLevel 66Reading a rectangle with sides (2x+3) and (2x-3) as a difference of squares, what is its area?ExpertLevel 66Which area partition in a square of side \(p+q\) represents the identity \((p+q)^2\)?ExpertLevel 66In a square of side (a+b), area partition is used instead of diagonal cutting. Which statement is correct?ExpertLevel 66A model shows (x^2+8x+15) and (x^2+8x+16) together. How much larger is the second than the first?ExpertLevel 66Which visual model can prove (49a^2-70ab+25b^2) as a perfect square?ExpertLevel 66If the rectangle model of (x^2+mx+56) is formed by (x+7) and (x+8), what are the two middle strips?ExpertLevel 66In a visual model, ((x-3)^2) is subtracted from ((x+3)^2). If seen as strips, how many (3x) strips remain?ExpertLevel 66Which rectangle model correctly represents (2x^2+x-15)?ExpertLevel 66In which visual model can (a^2+2ab+b^2-c^2) be changed into two rectangle sides?ExpertLevel 66A square board has side (x+4). A central square of side (x-4) is left empty. What is the border area?ExpertLevel 66In a grid, the columns are (x), (2), and the rows are (3x), (-5). What total area is formed?ExpertLevel 66If in the model of (x^2+2xy+y^2), only one (xy) rectangle is mistakenly taken, what wrong result will be obtained?ExpertLevel 66Which identity is most suitably shown by adding two differently shaded strips to a single (a) by (a) square?ExpertLevel 66